Change color by radius
Your node setup looks correct, although it could be made slightly less verbose by making use of the Vector Math: distance node.



I've managed to make it work on a torus. Perhaps you should try:


Making sure the origin is in the centre of the ring.
Tweaking the ColourRamp slider's Pos values so that the results of the previous node operations fall in their vicinity. As of right now, yours are set to 0 and 0.077, it seems; for me the spot was around 0.9 .